Numerous puzzles are based on the principle of “recombination”: manipulating pieces along constrained paths to reach a “solution state”. A traditional example is the puzzle consisting of fifteen square pieces that can slide along their edges, held in place by a square tray whose sides are four times the length of the squares. As one attempts to move a piece to its desired location, one is forced to move other pieces out of the way which prevent one from achieving the solution directly.
A second famous example is “Rubik's Cube,” whereby pieces are twisted around a cubic shape. Again, as one attempts to get certain pieces into a desired location, one is forced to move other pieces.